{"id":"e2765118-a508-44e1-b51a-53039eed032e","arxiv_id":"2507.12150","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In lead islands smaller than about 12 nm radius, Coulomb charging energy exceeds the pairing gap, enabling stable odd-parity ground states that can be locally tuned with STM voltage pulses.","lead":"Researchers used a scanning tunneling microscope to measure and locally tune the balance between charging energy and superconductivity in individual lead islands on graphene. They show that below a critical size, an odd number of electrons becomes the stable ground state, and this state can be switched by voltage pulses, a step toward parity-based qubits.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Parity tunability is inferred, not demonstrated: gate sweeps are shown only for islands with EC<Δ; the single odd-parity island is static.","rationale":"I read the paper as an experimental demonstration that Coulomb blockade can dominate pairing in small Pb islands and that electrostatic potentials can be locally modified. The DBTJ model is standard and the magnetic-field evolution in Fig. 5(d), showing gap reopening, is a nice signature consistent with an odd-parity ground state for the 9.5 nm island. The size-dependent extraction of EC and Δ (Fig. 2c) is model-dependent, as the reader notes, but the qualitative ordering (smaller islands have larger EC and smaller Δ) is robust. However, the article's central assertion and title promise local control of parity. The evidence for control consists of (i) q0 manipulation on large islands and (ii) a static odd-parity state on one small island. These pieces are never combined. A controlled gate sweep of the sub-12 nm island would close this gap; its absence means the strongest claim is underdetermined. The reader's weakest_assumption identifies a real technical risk in parameter extraction, but it is secondary: even if EC and Δ were known exactly, the 'tunable' part of the central claim would still lack direct support. Therefore my concern is distinct from the reader's, and the conditional verdict remains appropriate pending the proposed check or a softened conclusion.","tokens_in":8986,"tokens_out":5865,"duration_ms":67286,"concrete_test":"Select a Pb island with reff<12 nm, and apply the same voltage-pulse sequence used in Fig. 3(a) to sweep its residual charge q0 across at least one full electron (e.g., from 0 to e and back). Record dI/dV maps after each pulse, and track the evolution of the α and β excitation peaks. If the spectra reversibly switch from the even-parity pattern (symmetric gap, only α peaks) to the odd-parity pattern (appearance of β peaks, gap width 2(EC−Δ)) and back, the parity-tunability claim is directly supported. If the island instead remains in one parity or undergoes an irreversible switch, the manuscript should be revised to claim only 'odd-parity ground states observed' and 'q0 tunability demonstrated in the even-parity regime', with parity tuning left as a model prediction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim states that below reff≈12 nm, even- and odd-parity ground states coexist and can be tuned with electrostatic gating. The experimental support splits into two disjoint observations. First, voltage-pulse control of q0 is demonstrated on a 26.8 nm island (Fig. 3a) and mapped on islands with reff≥15 nm (Fig. 3c, Fig. 4), all in the EC<Δ regime where the ground state remains even at every q0. Second, the existence of an odd-parity ground state is shown for one island with reff=9.5 nm (Fig. 5c,d) at its ambient, uncontrolled q0. No measurement shows the same sub-12 nm island being swept through q0 across the even/odd degeneracy at q0=e. Thus the phrase 'coexist and can be tuned with electrostatic gating' is an extrapolation from the DBTJ model (Fig. 2d) plus separate observations, not a direct experimental result. This is the most load-bearing weakness because it targets the headline claim itself: even if the EC/Δ extraction is completely correct, the paper has not demonstrated local parity control; it has demonstrated a static parity state and q0 control in a different regime. The magnetic-field reopening signature (Fig. 5d) is convincing evidence for an odd-parity ground state at ambient q0, but it says nothing about tunability.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports STS measurements on Pb nano-islands grown on graphene, aimed at separating charging energy (EC) and superconducting pairing energy (Δ) in the double-barrier tunneling junction (DBTJ) regime. From the magnetic-field evolution of the spectral gap, the authors extract EC and Δ for 18 islands and assert a crossover at effective radius r_eff ≈ 12 nm below which EC > Δ. They further show that voltage pulses from the STM tip can alter the residual charge q0 of larger islands (r_eff ≥ 15 nm), producing gate-dependent spectral maps interpreted with the DBTJ model. For one small island (r_eff = 9.5 nm), they observe a gap that first closes and then reopens with magnetic field, which they identify as the signature of an odd-parity ground state. The paper concludes that even- and odd-parity ground states coexist below 12 nm and can be tuned with electrostatic gating.","tokens_in":9305,"tokens_out":3381,"duration_ms":44592,"significance":"If fully supported, the result would establish a surface-supported platform for parity control in superconducting islands, relevant for Majorana-box and parity-based qubit proposals. The work has clear strengths: the DBTJ model is standard and not invented for this paper; the magnetic-field-induced gap reopening in Fig. 5(d) is a distinctive, falsifiable signature of an odd-parity ground state; and the demonstration of local q0 control via STM voltage pulses (Fig. 3) is a useful technical advance. The spatial mapping in Fig. 4 also provides a creative way to visualize electrostatic puddle effects. However, the central claim of tunable parity is weakened by the fact that the gate-tuned maps and the odd-parity island are disjoint observations, and by the absence of error bars or robustness analysis in the extraction of EC and Δ. The significance of the paper depends on whether the authors can either supply the missing direct demonstration or appropriately soften the headline claim.","major_comments":[{"comment":"","section":"§Locally gating the Pb islands with voltage pulses; Figs. 3 and 5"},{"comment":"","section":"Fig. 2(b,c) and the extraction of EC and Δ from magnetic-field data"},{"comment":"","section":"Fig. 5(d) and the identification of odd parity"}],"minor_comments":[{"comment":"","section":"Abstract and Introduction"},{"comment":"","section":"Fig. 3 caption and text"},{"comment":"","section":"Fig. 5(c) and related text"},{"comment":"","section":"Introduction, first paragraph"},{"comment":"","section":"Fig. 2(c) caption"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely from a capable experimental group and the raw observations are interesting. However, I would advise the editor that the current wording of the conclusions overstates the evidence for parity tunability. The requested direct measurement (gate sweep on a sub-12 nm island) might be challenging, but it is the natural next step; alternatively, the authors can reframe the conclusions to distinguish between demonstrated q0 control in the even-parity regime and a model-supported prediction of tunability in the odd-parity regime. The missing error analysis for Fig. 2(c) is also essential before the quantitative crossover can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: this is a solid STM study of Pb islands on graphene, but the headline overreaches. The paper demonstrates two separate things: (1) voltage-pulse control of the residual charge q0 on islands with EC<Δ (where the ground state is always even), and (2) a static odd-parity ground state on one island with reff=9.5 nm, identified by the magnetic-field-induced gap reopening. It never shows the same small island being swept through the even/odd degeneracy at q0=e. So the claim that 'even-odd parity ground states coexist and can be tuned with electrostatic gating' is an inference from the DBTJ model plus two disjoint observations, not a direct experimental result.\n\nWhat is genuinely new is the use of STM voltage pulses as a local gate for supported superconducting islands, and the spatial mapping of the charge landscape via the ±α/±β peak intensities. The field-evolution method to disentangle EC and Δ is reasonable, and the gap-reopening signature in Fig. 5d is a clean, distinctive indicator of an odd-parity ground state. The DBTJ fits look careful, and the size dependence of EC and Δ in Fig. 2c tells a coherent story.\n\nSoft spots, in order of importance. The missing direct demonstration of parity tunability is the load-bearing issue; it is fixable by gating a sub-12 nm island or by softening the wording. Second, Fig. 2c has no error bars, and the critical radius of 12 nm is derived from the crossing of those two fitted trends. Third, only one island is shown in the odd-parity regime. Fourth, the extraction assumes EC is field-independent and that the tip gap closes at 0.8 T; those are plausible but not proven, and a small shift in EC would move the crossover radius.\n\nNone of this invalidates the static parity observation, which I find convincing. But the central claim as stated is not yet demonstrated.\n\nBottom line: worth a serious referee, not a desk reject. I would ask the authors to either provide gate-dependent data on a sub-12 nm island or explicitly rephrase the conclusion to say that odd-parity states exist and q0 can be tuned in the even-parity regime. With that change, this becomes a nice experimental letter.\n\nFor my own work, I would not cite it as a demonstration of parity control, but I would keep it in mind for the STM gating technique.","headline":"Clean static odd-parity signature in one small Pb island, but the advertised local parity control is an extrapolation from separate measurements.","tokens_in":9793,"tokens_out":2827,"would_cite":false,"duration_ms":31431,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"On individual lead islands with effective radius below about 12 nm, the energy $E_C$ to add one electron exceeds the Cooper-pair binding energy $\\Delta$, so the superconducting ground state can be flipped between even and odd…","keywords":["superconducting islands","Coulomb blockade","charge parity","even-odd ground states","scanning tunneling spectroscopy","lead islands on graphene","magnetic field gap reopening","electrostatic gating"],"falsifier":"Repeat the magnetic-field sweep on the 9.5 nm island with a normal-metal tip, so no tip superconducting gap is present: the zero-field spectral gap should be $2(E_C-\\Delta)$ and the high-field gap $2E_C$ if the odd-parity assignment is right, whereas a gap that simply closes without reopening would point to an even-parity state or to a field-dependent $E_C$.","tokens_in":8833,"feed_emoji":"⚛️","tokens_out":11305,"duration_ms":115266,"temperature":0.7,"pith_summary":"The paper reports that on individual superconducting lead islands sitting on graphene, the charging energy $E_C$ and the pairing gap $\\Delta$ can be measured separately, and the ground-state parity of the island can be switched locally. Using scanning tunneling spectroscopy fitted with a double-barrier tunneling junction model, the authors find that below an effective radius of about 12 nm, $E_C$ exceeds $\\Delta$. In that regime the ground state can be either even (all electrons paired) or odd (one unpaired electron) depending on the island's residual charge $q_0$, and STM voltage pulses move that charge in a controlled way. The odd-parity state is identified by a magnetic-field-induced reopening of the spectral gap after the tip's superconductivity is quenched. If correct, this establishes a surface-supported, locally gate-tunable superconducting island whose parity and charge can be controlled with a single tip.","feed_headline":"Tip voltage flips nanoscale lead islands into odd-parity states","feed_subtitle":"Below that size, charging energy beats pairing, and bias pulses flip the island's ground-state parity.","key_machinery":"The carrying object is the double-barrier tunneling junction (DBTJ) Hamiltonian for a small superconducting island, $H = H_S + H_C$, where the pairing term $H_S$ adds the pairing energy $\\Delta$ when the island's electron number is odd, and the charging term is $H_C = E_C(n - q_0/e)^2$ with $n$ the island charge and $q_0$ the gate-controlled residual charge. Its eigenstates form parabolas in $q_0$, with odd-parity parabolas shifted upward by $\\Delta$; when $E_C > \\Delta$, the odd-parabola minimum drops below the even one at $q_0 = e$, making the odd ground state accessible. The experimental protocol separates the two energies through the magnetic-field evolution: the tip gap closes first near 0.8 T and the island gap near 1.5 T, so the residual gap at high field equals $E_C$. STM voltage pulses then act as the local gate that moves $q_0$ and drives the parity crossing.","core_discovery":"On the paper's own terms, the central discovery is a size-controlled crossover in supported superconducting Pb islands: for effective radii above about 12 nm the pairing gap $\\Delta$ dominates the charging energy $E_C$, while below it $E_C > \\Delta$, and the even- and odd-parity ground states become nearly degenerate near residual charge $q_0 = e$. The authors demonstrate on a 9.5 nm island that the ground state can be odd: the spectral gap first closes as the tip's superconductivity is suppressed by magnetic field and then reopens as the bare Coulomb gap is restored, which is the predicted hallmark of an odd-parity state. They further show that repeated STM bias pulses shift the island's residual charge by more than one electron charge, reversibly moving the spectrum through the even/odd crossing and mapping the charge-parity landscape of an individual island.","pith_inferences":["The field-reopening signature could serve as a general spectroscopic fingerprint of odd-parity ground states in other superconducting islands, even where a full DBTJ fit is not available.","Because the island's residual charge responds to static charge puddles in the graphene, the same islands could act as scanning point-charge sensors, with the local potential landscape read out through the imbalance of the $\\alpha$ and $\\beta$ spectral peaks.","If the crossover radius is set by the ratio $E_C/\\Delta$ rather than lead-specific parameters, similar parity-tunable islands should appear in other strong-coupling superconductors on low-capacitance supports; growing islands of other materials at different sizes would test this.","Combined with spin-orbit coupling or a magnetic field tuned to the parity degeneracy point, the odd-parity island would form a two-level system whose charge and parity both respond to the tip; whether this becomes a usable qubit is not demonstrated in the paper."],"forward_implications":["Below the critical size, an island at $q_0 = e$ can sit in an odd-parity ground state, identified by the high-field reopening of its spectral gap.","Voltage-pulse gating provides local electrostatic control without a three-terminal gate, so the same island can be switched repeatedly between even and odd parity.","The magnetic-field protocol separates $E_C$ from $\\Delta$ in a single island, so the measured spectral gap no longer conflates the two energies.","Smaller islands enter a Coulomb-dominated regime where pairing alone no longer fixes the ground state, linking the data to the breakdown of Cooper pairing at the nanoscale.","The tunable even/odd platform is proposed by the authors as a basis for $\\pi$-junction superconducting devices and for parity-based or topological qubit designs."],"supporting_citations":[{"why":"Supplies the fit that captures the sequential closing of the tip and island gaps, from which $E_C$ is extracted at high magnetic field.","marker":"[18]"},{"why":"Earlier observation of a Coulomb gap plus enhanced superconducting gap in nanosized Pb islands; it underpins the identification of the field-independent residual gap as $E_C$.","marker":"[34]"},{"why":"Establishes magnetic-field gap reopening as the signature of an odd-parity superconducting ground state, the criterion used to label the 9.5 nm island.","marker":"[37]"},{"why":"Provides the parity-dependent theory in which an odd electron count costs an extra $\\Delta$, the basis of the even/odd ground-state competition.","marker":"[12]"},{"why":"Gives the even-odd parity effect on tunneling through a superconducting grain, used to interpret the $\\alpha$ and $\\beta$ excitation peaks.","marker":"[13]"},{"why":"Introduces single-electron charging of a superconducting island and underlies the DBTJ energy balance between $E_C$ and $\\Delta$.","marker":"[28]"},{"why":"Shows that STM voltage pulses can locally gate objects on graphene, the mechanism used here to tune the residual charge $q_0$.","marker":"[35]"}],"fun_headline_variants":["Voltage pulses map charge-parity states in lead nano-islands","Odd-parity ground states switched on in superconducting islands","Below 12 nm, lead islands flip between even and odd parity","STM pulses tune parity in nanoscale superconductors","Charge-parity landscape mapped for single superconducting island"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The 12 nm crossover and the odd-parity classification of the 9.5 nm island rest on assuming that $E_C$ is independent of magnetic field and that the tip gap is what closes near 0.8 T, leaving a high-field residual gap equal to $E_C$; if $E_C$ shifts with field or the closing order is misread, the critical size and the parity label could change.","fun_headline_variants_meta":{"raw":{"variants":["Voltage pulses map charge-parity states in lead nano-islands","Odd-parity ground states switched on in superconducting islands","Below 12 nm, lead islands flip between even and odd parity","STM pulses tune parity in nanoscale superconductors","Charge-parity landscape mapped for single superconducting island"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000647,"raw_usage":{"total_tokens":2903,"prompt_tokens":806,"completion_tokens":2097,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":422,"completion_tokens_details":{"reasoning_tokens":2017}},"tokens_in":422,"tokens_out":2097,"duration_ms":15089,"temperature":1.0,"reasoning_tokens":2017,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T16:52:01.630832+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the magnetic-field sweep on the 9.5 nm island with a normal-metal tip, so no tip superconducting gap is present: the zero-field spectral gap should be $2(E_C-\\Delta)$ and the high-field gap $2E_C$ if the odd-parity assignment is right, whereas a gap that simply closes without reopening would point to an even-parity state or to a field-dependent $E_C$.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the fit that captures the sequential closing of the tip and island gaps, from which $E_C$ is extracted at high magnetic field."},{"cited_title":"Observation of Coulomb Gap and Enhanced Superconducting Gap in Nano-Sized Pb Islands Grown on SrTiO 3,","cited_arxiv_id":null,"evidence_quote":"Earlier observation of a Coulomb gap plus enhanced superconducting gap in nanosized Pb islands; it underpins the identification of the field-independent residual gap as $E_C$."},{"cited_title":"Parity transitions in the super- conducting ground state of hybrid InSb–Al Coulomb is- lands,","cited_arxiv_id":null,"evidence_quote":"Establishes magnetic-field gap reopening as the signature of an odd-parity superconducting ground state, the criterion used to label the 9.5 nm island."},{"cited_title":"Parity-induced suppression of the Coulomb blockade of Josephson tunneling,","cited_arxiv_id":null,"evidence_quote":"Provides the parity-dependent theory in which an odd electron count costs an extra $\\Delta$, the basis of the even/odd ground-state competition."},{"cited_title":"Ef- fects of Charge Parity in Tunneling Through A Supercon- ducting Grain,","cited_arxiv_id":null,"evidence_quote":"Gives the even-odd parity effect on tunneling through a superconducting grain, used to interpret the $\\alpha$ and $\\beta$ excitation peaks."},{"cited_title":"Single-electron charg- ing of a superconducting island,","cited_arxiv_id":null,"evidence_quote":"Introduces single-electron charging of a superconducting island and underlies the DBTJ energy balance between $E_C$ and $\\Delta$."},{"cited_title":"Gate- controlled ionization and screening of cobalt adatoms on a graphene surface,","cited_arxiv_id":null,"evidence_quote":"Shows that STM voltage pulses can locally gate objects on graphene, the mechanism used here to tune the residual charge $q_0$."}],"review_version":1}